{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning to Throw\n",
    "\n",
    "[![Google Collab Book](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/tum-pbs/PhiFlow/blob/develop/examples/optim/Learn_Throw.ipynb)\n",
    "\n",
    "This example trains neural networks to solve inverse throwing problems.\n",
    "Check out the corresponding [optimization](https://tum-pbs.github.io/PhiFlow/examples/optim/Optimize_Throw.html) example which finds the optimal trajectory using gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install --quiet phiflow\n",
    "from phi.torch.flow import *\n",
    "# from phi.flow import *  # If JAX is not installed. You can use phi.jax or phi.tf as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define the "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate_hit(pos, height, vel, angle, gravity=1.):\n",
    "    vel_x, vel_y = math.cos(angle) * vel, math.sin(angle) * vel\n",
    "    height = math.maximum(height, .01)\n",
    "    hit_time = (vel_y + math.sqrt(vel_y**2 + 2 * gravity * height)) / gravity\n",
    "    return pos + vel_x * hit_time, hit_time, height, vel_x, vel_y\n",
    "\n",
    "def sample_trajectory(pos, height, vel, angle, gravity=1., steps=spatial(time=100)):\n",
    "    _, hit_time, height, vel_x, vel_y = simulate_hit(pos, height, vel, angle, gravity)\n",
    "    t = math.linspace(0, hit_time, steps)\n",
    "    return vec(x=pos + vel_x * t, y=height + vel_y * t - gravity / 2 * t ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we generate a training set and test by sampling random values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_data(shape):\n",
    "  pos = math.random_normal(shape)\n",
    "  height = math.random_uniform(shape) + .5\n",
    "  vel = math.random_uniform(shape)\n",
    "  angle = math.random_uniform(shape) * PI/2\n",
    "  return math.stack(dict(pos=pos, height=height, vel=vel, angle=angle), channel('vector'))\n",
    "\n",
    "x_train = generate_data(batch(example=1000))\n",
    "x_test = generate_data(batch(example=1000))\n",
    "y_train = simulate_hit(*x_train.vector)[0]\n",
    "y_test = simulate_hit(*x_test.vector)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We set up two networks with identical initialization, one for supervised training and one for diff.phys. training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "math.seed(0)\n",
    "net_sup = dense_net(1, 4, [32, 64, 32])\n",
    "math.seed(0)\n",
    "net_dp = dense_net(1, 4, [32, 64, 32])\n",
    "math.assert_close(get_parameters(net_sup)['linear1.weight'], get_parameters(net_dp)['linear1.weight'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Supervised Training\n",
    "Now we can train the network. We feed the desired hit position into the network and predict a possible initial state.\n",
    "For supervised training, we compare the network prediction to the ground truth from our training set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial supervised loss (test set): (\u001b[92m(exampleᵇ=1000)\u001b[0m \u001b[94m1.620 ± 0.860\u001b[0m \u001b[37m(3e-01...7e+00)\u001b[0m, \u001b[92m(exampleᵇ=1000, vectorᶜ=4)\u001b[0m \u001b[94m0.007 ± 0.026\u001b[0m \u001b[37m(-8e-02...2e-01)\u001b[0m)\n",
      "Final supervised loss (test set): (\u001b[92m(exampleᵇ=1000)\u001b[0m \u001b[94m0.282 ± 0.185\u001b[0m \u001b[37m(1e-02...1e+00)\u001b[0m, \u001b[92m(exampleᵇ=1000, vectorᶜ=4)\u001b[0m \u001b[94m0.571 ± 0.588\u001b[0m \u001b[37m(-3e+00...3e+00)\u001b[0m)\n"
     ]
    }
   ],
   "source": [
    "opt_sup = adam(net_sup)\n",
    "\n",
    "def supervised_loss(x, y, net=net_sup):\n",
    "  prediction = math.native_call(net, y)\n",
    "  return math.l2_loss(prediction - x), prediction\n",
    "\n",
    "print(f\"Initial supervised loss (test set): {supervised_loss(x_test, y_test)}\")\n",
    "\n",
    "sup_pred_trj = []\n",
    "for i in range(200):\n",
    "  update_weights(net_sup, opt_sup, supervised_loss, x_train, y_train)\n",
    "  sup_pred_trj.append(math.native_call(net_sup, y_test))\n",
    "\n",
    "print(f\"Final supervised loss (test set): {supervised_loss(x_test, y_test)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While there is progress, the final loss is not great.\n",
    "Feel free to run more iterations but there is a deeper problem at work here.\n",
    "Before we get into that, let's train a the network again but with a differentiable physics loss function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## End-to-end Training with Differentiable Physics\n",
    "For the differentiable physics loss, we simulate the trajectory given the initial conditions predicted by the network. Then we can measure how close to the desired location the network got."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial supervised loss (test set): (\u001b[92m(exampleᵇ=1000)\u001b[0m \u001b[94m1.620 ± 0.860\u001b[0m \u001b[37m(3e-01...7e+00)\u001b[0m, \u001b[92m(exampleᵇ=1000, vectorᶜ=4)\u001b[0m \u001b[94m0.007 ± 0.026\u001b[0m \u001b[37m(-8e-02...2e-01)\u001b[0m)\n",
      "Final supervised loss (test set): (\u001b[92m(exampleᵇ=1000)\u001b[0m \u001b[94m1.154 ± 0.684\u001b[0m \u001b[37m(7e-02...4e+00)\u001b[0m, \u001b[92m(exampleᵇ=1000, vectorᶜ=4)\u001b[0m \u001b[94m0.196 ± 0.479\u001b[0m \u001b[37m(-2e+00...2e+00)\u001b[0m)\n"
     ]
    }
   ],
   "source": [
    "opt_dp = adam(net_dp)\n",
    "\n",
    "def physics_loss(y, net=net_dp):\n",
    "  prediction = math.native_call(net, y)\n",
    "  y_sim = simulate_hit(*prediction.vector)[0]\n",
    "  return math.l2_loss(y_sim - y)\n",
    "\n",
    "print(f\"Initial supervised loss (test set): {supervised_loss(x_test, y_test, net=net_dp)}\")\n",
    "\n",
    "dp_pred_trj = []\n",
    "for i in range(200):\n",
    "  update_weights(net_dp, opt_dp, physics_loss, y_train)\n",
    "  dp_pred_trj.append(math.native_call(net_dp, y_test))\n",
    "\n",
    "print(f\"Final supervised loss (test set): {supervised_loss(x_test, y_test, net=net_dp)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks even worse! The differentiable physics network seems to stray even further from the ground truth.\n",
    "Well, we're not trying to match the ground truth, though. Let's instead measure how close to the desired location the network threw the object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Supervised network (test set): \u001b[92m(exampleᵇ=1000)\u001b[0m \u001b[94m0.004 ± 0.003\u001b[0m \u001b[37m(2e-03...4e-02)\u001b[0m\n",
      "Diff.Phys. network (test set): \u001b[92m(exampleᵇ=1000)\u001b[0m \u001b[94m3.16e-05 ± 7.9e-05\u001b[0m \u001b[37m(1e-11...2e-03)\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "print(f\"Supervised network (test set): {physics_loss(y_test, net=net_sup)}\")\n",
    "print(f\"Diff.Phys. network (test set): {physics_loss(y_test, net=net_dp)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is much more promissing. The diff.phys. network seems to hit the desired location very accurately considering it was only trained for 200 iterations. With more training steps, this loss will go down even further, unlike the supervised network.\n",
    "\n",
    "So what is going on here? Why does the supervised network perform so poorly?\n",
    "The answer lies in the problem itself. The task is multi-modal, i.e. there are many initial states that will hit the same target.\n",
    "The network only gets the target position and must decide on a single initial state. With supervised training, there is no way to know which ground truth solution occurs in the test set. The best the network can do is average nearby solutions from the training set. But since the problem is non-linear, this will give only a rough guess.\n",
    "\n",
    "The diff.phys. network completely ignores the ground truth solutions which are not even passed to the `physics_loss` function. Instead, it learns to hit the desired spot, which is exactly what we want.\n",
    "\n",
    "We can visualize the difference by looking at a couple of example trajectories."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\phd\\phiflow2\\phiml\\phiml\\math\\_shape.py:2048: RuntimeWarning: Stacking shapes with incompatible item names will result in item names being lost. For vector Got ('pos', 'height', 'vel', 'angle') and None\n",
      "  warnings.warn(f\"Stacking shapes with incompatible item names will result in item names being lost. For {name} Got {item_names[index]} and {items}\", RuntimeWarning)\n"
     ]
    },
    {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x21b21c0db20>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt_trjs = stack({\n",
    "    \"Ground truth\": x_test,\n",
    "    \"Supervised\": stack(sup_pred_trj, batch('iter')),\n",
    "    \"Diff.Phys.\": stack(dp_pred_trj, batch('iter'))\n",
    "}, channel('type'))\n",
    "plot(sample_trajectory(*opt_trjs.example[:4].iter[::4].vector), animate='iter')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the final state we can see that the differentiable physics network matches the hit point much more precisely than the supervised network, as expected from the loss values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 864x360 with 16 Axes>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x360 with 16 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(sample_trajectory(*opt_trjs.example[:4].iter[-1].vector))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "phiflow2",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
